What is the value of 2(cos(pi/6)+isin(pi/6))*5(cos(pi/3)+isin(pi/3)) ?

The value of 2(cos(pi/6)+isin(pi/6))*5(cos(pi/3)+isin(pi/3)) is 10i

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2(cos(pi/6)+isin(pi/6))*5(cos(pi/3)+isin(pi/3))

2 (cos (\frac{π}{6}) + i sin (\frac{π}{6})) \cdot 5 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))

10 i

Solution steps

2 (cos (\frac{π}{6}) + i sin (\frac{π}{6})) \cdot 5 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

Use the following trivial identity:

sin (\frac{π}{6}) = \frac{1}{2}

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= 2 (\frac{3}{2} + i \frac{1}{2}) \cdot 5 (\frac{1}{2} + i \frac{3}{2})

Simplify

2 (\frac{3}{2} + i \frac{1}{2}) \cdot 5 (\frac{1}{2} + i \frac{3}{2}) : 10 i

= 10 i

185 sin (1 5^{\circ})

\frac{1}{sin ( 12 0 ^{\circ} )}

cos (\frac{4 π}{3}) + i \cdot sin (\frac{4 π}{3})

arccos (\frac{2}{3 2})

- 2 cos (- 2 π)

What is the value of 2(cos(pi/6)+isin(pi/6))*5(cos(pi/3)+isin(pi/3)) ?
The value of 2(cos(pi/6)+isin(pi/6))*5(cos(pi/3)+isin(pi/3)) is 10i